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Computational Methods in Systems and Control Theory

MPI project together with the Department of Mathematics, Virginia Tech.

Interpolatory Methods for Parametric Model Reduction

Project director: Researcher: Duration: since 02/2009

Project description:
Model order reduction is known to be an efficient tool for replacing very large dynamical systems in numerical simulations by systems of much smaller dimension keeping a desired accuracy in the approximation of the original system response. However, significant modifications to the underlying physical model such as geometric variations, changes in material properties, or alterations in boundary conditions are usually not reflected in the reduced-order system. This motivates the development of new model reduction methods which are supposed to preserve the parametric dependence of the original system in the reduced-order model. In this project, we derive a unifying projection-based framework for structure-preserving interpolatory model reduction of parameterized linear dynamical systems which do structurally depend (linear or nonlinear) on parameters. We are seeking for conditions under which the gradient and Hessian of the system response with respect to the system parameters are matched in the reduced-order model. Moreover, we will investigate the optimal choice of interpolation data for computing reduced-order models which are optimal with respect to a joint error measure (w.r.t. parameter and frequency domain).

Related publications:

author = {U. Baur and C. A. Beattie and P. Benner and S. Gugercin},
title = {Interpolatory Projection Methods for Parameterized Model Reduction},
journal = SIAMSciComp,
year = {2011},
volume = {33},
pages = {2489--2518},
number = {5} }
Interpolatory Projection Methods for Parameterized Model Reduction
Baur, Ulrike; Beattie, Christopher; Benner, Peter; Gugercin, Serkan;
SIAM J. Sci. Comput.  :  Vol. 33 of 5;

©2018, Max Planck Society, Munich
Jens Saak, saak@mpi-magdeburg.mpg.de
22 Oktober 2015